C++ implementations of numerical methods for solving differential-algebraic equations: Design and optimization considerations

ACM Transactions on Mathematical Software

Volumn 25, Issue 4, 1999, Pages 377-403

  Kees, Christopher E ^a,b   Miller, Cass T ^a,b  

^a UNIVERSITY OF NORTH CAROLINA   (United States)

^b University of North Carolina at Chapel Hill   (United States)

Author keywords

Algorithms; D.3.2 Programming Languages : Language classifications C++; Design; Differential algebraic equations; Experimentation; Fortran 77; Languages; Performance

Indexed keywords

EID: 0000253859     PISSN: 00983500     EISSN: None     Source Type: Journal    
DOI: 10.1145/332242.334001     Document Type: Article

References (39)

1. ANDERSON, E., BAI, Z., BISCHOF, C., DEMMEL, J., DONGARRA, J., Du CROZ, J., GREENBAUM, A., HAMMARLING, S., MCKENNEY, A., OSTROUCHOV, S., AND SORENSEN, D. 1994. LAPACK User's Guide Release 2.0. SIAM, Philadelphia, PA. http://www.netlib.org/lapack/lug/lapack lug.html
2. ARGE, E. ET AL. 1997. On the numerical efficiency of C++ in scientific computing. In Numerical Methods and Software Tools in Industrial Mathematics Birkhäuser Boston Inc., Cambridge, MA, 91-118.
3. BARTON, J. J. AND NACKMAN, L. R. 1994. Scientific and Engineering C++. Addison-Wesley, Reading, MA.
4. BECK, R., ERDMANN, B., AND ROITZSCH, R. 1995. KASKADE 3.0: An object-oriented adaptive finite element model. Tech. Rep. TR 95-4. Konrad-Zuse-Zentrum fur Informationstechnik, Berlin, Germany.
5. BESSON, J. AND FOERCH, R. 1997. Large scale object-oriented finite element code design. Comput. Methods Appl. Mech. Eng. 142, 1-2, 165-187.
6. BRENAN, K., CAMPBELL, S., AND PETZOLD, L. 1996. Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations. SIAM, Philadelphia, PA.
7. BROWN, P. N., HINDMARSH, A. C., AND PETZOLD, L. R. 1994. Using Krylov methods in the solution of large-scale differential-algebraic systems. SIAM J. Sci Comput. 15, 6 (Nov. 1994), 1467-1488. Also available as a technical report from Lawrence Livermore National Laboratory
8. BRUASET, A. M. AND LANGTANGEN, H. P. 1997. Object-oriented design of preconditioned iterative methods in diffpack. ACM Trans. Math. Softw. 23, 1, 50-80.
9. CARY, J. R., SHASHARINA, S. G., CUMMINGS, J. C., REYNDERS, J. V., AND HINKER, P. J. 1997. Comparison of C++ and Fortran 90 for object-oriented scientific programming. Comput. Phys. Commun. 105, 1, 20-36.
10. DECYK, V. K., NORTON, C. D., AND SZYMANSKI, B. K. 1997. Expressing object-oriented concepts in Fortran 90. SIGPLAN Fortran Forum 16, 1, 13-18.
11. DONESCU, P. AND LAURSEN, T. A. 1996. A generalized object-oriented approach to solving ordinary and partial differential equations using finite elements. Finite Elem. Anal. Des. 22, 1, 93-107.
12. DONGARRA, J., BUNCH, J., MOLER, C., AND STEWART, P. 1984. Linpack. (Software), http://www.netlib.org/linpack
13. DONGARRA, J. J., LUMSDAINE, A., NIU, X., POZO, R., AND REMINGTON, K. 1994. A sparse matrix library in C++ for high performance architectures. In Proceedings of the 2nd Annual Object-Oriented Numerics Conference (OON-SKI '94, Sun River, OR, Apr.), 214-218.
14. DONGARRA, J., LUMSDAINE, A., POZO, R., AND REMINGTON, K. 1996. ImL++ version 1.2 iterative methods library reference guide.
15. DONGARRA, J. J., POZO, R., AND WALKER, D. W. 1993. LAPACK++: A design overview of object-oriented extensions for high performance linear algebra. In Proceedings of the Conference on Supercomputing (Supercomputing '93, Portland, OR, Nov. 15-19), B. Borchers and D. Crawford, Eds. IEEE Computer Society Press, Los Alamitos, CA, 162-171.
16. DUBOIS-PELERIN, Y. AND PEGON, P. 1997. Improving modularity in object-oriented finite element programming. Commun. Numer. Methods Eng. 13, 3, 193-198.
17. DUBOIS-PÈLERIN, Y., ZIMMERMANN, T., AND BOMME, P. 1992. Object-oriented finite element in programming: II. A prototype program in Smalltalk. Comput. Methods Appl. Mech. Eng. 98, 3 (Aug. 1992), 361-397.
18. EYHERAMENDY, D. AND ZIMMERMANN, T. 1996. Object-oriented finite elements: II. A symbolic environment for automatic programming. Comput. Methods Appl. Mech. Eng. 132, 3-4, 277-304.
19. GEAR, C. 1971. The simultaneous numerical solution of differential-algebraic equations. IEEE Trans. Circuit Theory CT-18, 89-95.
20. GEAR, C. W. 1973. Asymptotic estimation of errors and derivatives for the numerical solution of ordinary differential equations. Tech. Rep. 598. Department of Computer Science, University of Illinois at Urbana-Champaign, Urbana, IL.
21. GEAR, C. 1986. Differential-algebraic equation index transformations. University of Illinois at Urbana-Champaign, Champaign, IL.
22. GEAR, C., LEIMKUHLER, B., AND GUPTA, G. 1985. Automatic integration of Euler-Lagrange equations with constraints. J. Comput. Appl. Math. 12 / 13 (May), 77-90.
23. JACKSON, K. R. AND SACKS-DAVIS, R. 1980. An alternative implementation of variable step-size multistep formulas for stiff ODEs. ACM Trans. Math. Softw. 6, 3 (Sept.), 295-318.
24. KARAMETE, B., TOKDEMIR, T., AND GER, M. 1997. Unstructured grid generation and a simple triangulation algorithm for arbitrary 2-D geometries using object-oriented programming. Int. J. Num. Methods Eng. 40, 2, 251-268.
25. KELLEY, C. 1995. Iterative Methods for Linear and Nonlinear Equations. SIAM, Philadelphia, PA.
26. KELLEY, C. T., MILLER, C. T., AND TOCCI, M. D. 1998. Termination of Newton/Chord iterations and the methods of lines. SIAM J. Sci. Comput. 19, 1, 280-290.
27. LEIMKUHLER, B. J. 1988. Approximation methods for the consistent initialization of differential-algebraic equations. Ph.D. Dissertation. University of Illinois at Urbana-Champaign, Champaign, IL.
28. LEWIS, R., MASTERS, I., AND CROSS, J. 1997. Automatic timestep selection for the super-time-stepping acceleration on unstructured grids using object-oriented programming. Commun. Numer. Methods Eng. 13, 3, 249-260.
29. LIU, J.-L., LIN, L-J., SHIH, M.-Z., CHEN, R.-C., AND HSIEH, M.-C. 1996. Object-oriented programming of adaptive finite element and finite volume methods. Appl. Numer. Math. 21, 4, 439-467.
30. MAIER, R. S. AND PETZOLD, L. R. 1993. User's guide to DASPKMP and DASPKF90. Army High Performance Computing Research Center, Minneapolis, MN.
31. MALY, T. AND PETZOLD, L. R. 1996. Numerical methods and software for sensitivity analysis of differential-algebraic systems. Appl. Numer. Math. 20, 1-2, 57-79.
32. NEWCOMB, R. W. 1981. The semistate description of nonlinear and time-variable circuits. IEEE Trans. Circ. Syst. 28, 1, 203-216.
33. PETZOLD, L. 1983. A Description of DASSL: A Differential / Algebraic System Solver. North-Holland Publishing Co., Amsterdam, The Netherlands.
34. QUATRANI, T. 1998. Visual Modeling with Rational Rose and UML. Addison Wesley object technology series. Addison-Wesley Longman Publ. Co., Inc., Reading, MA.
35. ROBISON, A. D. 1996. C++ gets faster for scientific computing. Comput. Physics 10, 5, 458-462.
36. STROUSTRUP, B. 1997. The C++ Programming Language. 3rd ed. Addison-Wesley, Reading, MA.
37. TOCCI, M., KELLEY, C., AND MILLER, C. 1997. Accurate and economical solution of the pressure-head form of Richards' equation by the method of lines. Adv. Water Resour. 20, 1, 1-14.
38. ZIMMERMAN, T. AND EYHERAMENDY, D. 1996. Object-oriented finite elements I. Principles of symbolic derivations and automatic programming. Comput. Methods Appl. Mech. Eng. 132, 3-4, 259-276.
39. ZIMMERMANN, T., DUBOIS-PèLERIN, Y., AND BOMME, P. 1992. Object-oriented finite element programming: I. Governing principles. Comput. Methods Appl. Mech. Eng. 98, 2 (July 1992), 291-303.